Many reservoirs are highly fractured due to the complex tectonic movement and sedimentation process the formation has experienced. The permeability of a fracture is usually much larger than that of the surrounding rock matrix. As a result, the fluid will flow mostly through the fracture network, if the fractures are connected. This implies that the fracture connectivities and their distribution will largely determine fluid transport in a naturally fractured reservoir. Due to statistically complex distribution of geological heterogeneity and multiple length and time scales in natural porous media, three approaches are commonly used in describing fluid flow and solute transport in naturally fractured formations: (1) discrete fracture models, (2) continuum models using effective properties for discrete grids, and (3) hybrid models that combine discrete large features and equivalent continuum.
Currently, most reservoir simulators employ dual continuum formulations (i.e., dual porosity/permeability) for naturally fractured reservoirs, in which reservoir models comprising a grid of porous matrix blocks are divided by very regular fracture patterns. A primary input into these simulation models is the permeability of the fracture system assigned to the individual matrix blocks. The permeability can only be reasonably calculated if the fracture systems are regular and well connected. However, field characterization studies have shown that fracture systems are very irregular, often disconnected and occur in swarms. This dual porosity/permeability method is well known to be computationally inefficient and is inflexible with respect to capturing or honoring fracture characteristics in real reservoirs.
Most naturally fractured reservoirs include fractures of multiple length-scales. The effective matrix block permeability calculated by a conventional boundary element method becomes prohibitively expensive as the number of fractures increases. The calculated effective properties for matrix blocks also underestimates the properties for long fractures whose length scale is much larger than the dimensions of a matrix block.
S. H. Lee, M. F. Lough and C. L. Jensen, Hierarchical modeling of flow in naturally fractured formations: with multiple length scales, Water Resources Research, 37, 443-455, 2001, (hereafter referred to as Lee et al.) proposed a hierarchical method to model fluid flow in a reservoir with multiple-length scaled fractures. This Lee et al. reference is hereby incorporated by reference in its entirety. Lee et al. assumed that short fractures are randomly distributed and contribute to increasing the effective matrix permeability. An asymptotic solution representing the permeability contribution from short fractures was derived. With the short fracture contribution to permeability, the effective matrix permeability can be expressed in a general tensor form. Furthermore, Lee et al. also developed a boundary element method for Darcy's equation with tensor permeability. For medium-length fractures in a matrix block, a coupled system of Poisson equations with tensor permeability was solved numerically using a boundary element method. The matrix block effective permeabilities were used with a finite difference simulator to compute flow through the fracture system. The simulator was enhanced to use a control-volume finite difference formulation for general tensor permeability input (i.e., 9-point stencil for 2-D and 27-point stencil for 3-D). In addition, long fractures were explicitly modeled by using a transport index between a fracture and the porous matrix in a grid block.
Lee et al. modeled long fractures explicitly. In their work, the fracture length of the long fractures is much longer than the matrix block size but the fracture height is short (equivalent to the matrix block size). They applied the concept of well bore productivity index (PI) to derive a transport index to describe the fluid transport between fractures and matrix blocks, and then formulated fluid flow as a one-dimensional well-like equation inside the fracture and a source/sink term between the fracture and matrix blocks. Although using well-bore PI concept is a novel way to model long fractures explicitly and efficiently, their implementation has several limitations: (1) fractures are one-dimensional, (2) fractures are not connected, and (3) fractures do not intersect well bores. Furthermore, this method also fails to adequately honor fracture characteristics found in actual fractured reservoirs.
The present invention overcomes the shortcomings in the previous work of Lee et al. and others with regard to realistically modeling fluid flow in fractured reservoirs.